Determine the intercepts of the line. $ -5x-4y=10$ $y$ -intercept: $\Big($
Explanation: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}-5\cdot{0}-4y&=10\\ -4y&=10\\ y&=-2.5\end{aligned}$ So the $y$ -intercept is $\left(0,-2.5\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}-5x-4\cdot{0}&=10\\ -5x&=10\\ x&=-2\end{aligned}$ So the $x$ -intercept is $\left(-2,0\right)$. In conclusion, The $y$ -intercept is $\left(0,-2.5\right)$. The $x$ -intercept is $\left(-2,0\right)$.